Embedding Color Watermarks into Halftoning Images using Minimum-Distance Binary Patterns Pedro Garcia Freitas∗, Mylene` C.Q. Fariasy and Aleteia´ P. F. de Araujo´ z ∗zDepartment of Computer Science, yDepartment of Electrical Engineering, University of Bras´ılia, Brazil Email: ∗[email protected], [email protected], [email protected] Abstract—This paper presents a halftoning-based watermark- reconstructed image may present distortions like noise [16] ing method. This method enables the embedding of a color image and blur [17]. Therefore, PS processes make hardcopy water- into a binary black-and-white halftone, while maintaining the marking more challenging than digital watermarking. image quality. The proposed technique is capable of embedding watermarks of three color channels into a binary halftone. To Many works in the literature address the document hardcopy achieve high quality halftones, the method maps colors to halftone problem by trying to keep the hidden information on a PS channels with homogeneous dot patterns which in turn use channel more robust. Most prior work on image data hiding different binary texture orientations to carry the watermark. target color and grayscale images with a wide range of They are obtained by solving a minimization problem in which intensity values [18]–[20]. These methods differ from each the objective function is the binary distance between the original binary halftone and the available patterns. To restore the color other in terms of efficiency, capacity, and robustness. Brassil information, we scan the printed halftone image and compute et al. [21] propose authentication methods based on shift the inverse information (considering the dot pattern). Using coding. To increase the robustness, their methods require the the mapped information, we restore the original color channels use of uniformly spaced centroids, which are often difficult from the halftone images using a high-quality inverse halftoning to obtain. Tan et al. [22] extended these methods using a algorithm. Experimental results show that the method produces restorations with a superior quality than other methods found directional modulation technique for watermarking of Chinese in the literature and increases the embedding capacity. text images. More recently, other methods were proposed for specific applications [23]–[26]. Keywords-Embedding, Halftone, Color Restoration, Water- mark, Inverse Halftoning. Among the available methods, those that embed information into binary images are very promising because the pixel binarization is the last step process of the printing process. I. INTRODUCTION When the scanner reads the paper, the data is first collected Transmitting side information using printed media is a as a binarized halftone which increases the robustness of PS challenge due to the distortions introduced by the print- process. It is worth pointing out that, since binary images and-scan (PS) process [1]. Some of these distortions occur have less capacity to hide information, embedding data in because the displayed digital color may differ from its printed binary images is more difficult than in color or grayscale im- representation. One of the causes for these differences is the ages [27]. Although more difficult, the demand for this kind of fact that the digital image is converted to a halftone represen- technique is increasing and several binary-image watermarking tation before being printed [2]. This halftone representation techniques have been developed [28]–[32]. However, as stated is generated from a mathematical model that produces colors by Hou et al. [27], these methods have several limitations that using a combination of colored dot patterns [3]. The halftone include a limited data capacity and the presence of noticeable images are perceived as continuous tone images when viewed artifacts. from a distance due to a low-pass property of the Human Some approaches have been proposed to increase the em- Visual System (HVS). Many different halftoning methods have bedding capacity of binary-images embedding. Pan et al. been developed, including Direct Binary Search (DBS) [4, 5], propose a low-capacity watermarking scheme for halftone Ordered Dithering (OD) [6, 7], Error Diffusion (ED) [8]–[10], image authentication, exploiting an image hash as a fragile and Dot Diffusion (DD) [11]–[13]. Although there is a great watermark [33]. Guo and Liu [34] developed a higher ca- diversity of image halftoning methods, most of them modify pacity watermarking technique that uses a block truncation the coding information of the printing process. code. Son and Choo [35] proposed a watermarking method The scanning process performs the inverse task of the for clustered halftone dots in which the embedded binary printing process. Scanner devices read the printed halftone data is recovered using dictionary learning. Guo et al. [36] and restore a multi-level image via an inverse halftoning proposed a halftoning-based approach capable of embedding algorithm [14, 15]. Although the inverse halftoning algorithm watermarks using direct binary search to encode the binary recovers the distinct intensity levels of the original image, the data. Guo and Liu [37] propose a method for embedding a multi-tone watermark that, as a consequence, produces a lower channels. Each color channel of W is treated as a grayscale im- quality image. Although all these methods have a reasonable age and a halftoning algorithm is used to generate R = frijg, embedding data capacity, they are restricted to a specific type G = fgijg, and B = fbijg, where rij; gij; bij 2 f0; 1g. of dithering that limits their performance and application. Using a combination of each pixel of these binary channels, More recently, Son et al. proposed some techniques [38, 39] we map a binary mask that is used to encode the host halftone. to restore color channels from a black-and-white halftone The method, therefore, involves three steps: generation of image that has homogeneously distributed dot patterns. This masks, color encoding of the watermark, and restoration of work represents an improvement for the reversible color- the original color watermark (decoding). We describe these to-grayscale conversion problem [40]–[42]. This conversion three steps. problem is specific to watermarking techniques that aim to re- A. Mask Generation cover the original color channels from watermarked grayscale images submitted to a PS process. This application involves The encoding masks are generated by computing the finite a large amount of embedded data because it inserts two n-ary Cartesian Product of the set X that is defined as: chrominance images (color channels) into a luminance channel n n Y ∗ (grayscale image) [43]. X = X = f(x1; : : : ; xn): 8k 2 Nn : xk 2 Xg ; (2) Given these halftoning and watermarking challenges, we k=1 n propose a binary image watermarking method that uses min- where X is a set of all ordered n-tuples fxkg and each n imum distance of binary patterns. The method encodes color element xk is a basis element of X . For X = f0; 1g we images into dithering patterns of halftone images with a similar have a total of 2n distinct n-tuples. Each tuple is equivalent goal to the work done by Son et al. [38, 39]. However, contrary to a binary vector (defined in Eq. 1) and is used to map the to their algorithms, that only allow self-embedding of a color combinations of each pixel of a halftoned RGB channel. Since channels into its halftone version, the proposed algorithm is each pixel of the R, G, and B halftones has only two possible far more flexible and it is able to embed any content (another values, the result of this Cartesian product is a set of 23 = 8 image or itself). triplets. The rest of this paper is organized as follows. Section II Next, using Eq. 2, we compute a larger set of tuples to gives a brief overview of binary vector dissimilarity measures. represent the distribution of points in the halftone. The higher Section III describes the proposed method, detailing encoding the number of tuples, the larger is the distribution of distinct (embedding) and decoding (recovering) of watermarks. The dots, which means that there are more options to represent experimental results are presented in Section IV. Finally, the the distribution of original pixels in the grayscale halftone conclusions are drawn in Section V (i.e. higher fidelity to unmarked halftone). On the other hand, the more distinct tuples there are, the more space is required II. DISTANCE OF BINARY PATTERNS to represent them. For simplicity, in this paper we adopt A binary vector Z with n dimensions is defined as n = 9, which gives a total of 512 distinct nonuples. Since we have 8 distinct triplets and 512 distinct nonuplets, each Z = fz1; z2; ··· ; zng; (1) triplet is used to map a subset of these nonuplets. More where zk 2 f0; 1g, 8 k 2 f1; 2; : : : ; ng. Given two vectors specifically, each triplet tk maps a set of 64 distinct nonuplets k k k X 2 Ω and Y 2 Ω, where Ω is the set of all n-dimensional Lk = fl1 ; l2 ; ··· ; l64g. For our application, the nonuplets are binary vectors, let Sij, 8(i; j) 2 f0; 1g, be the number of geometrically distributed in 3 × 3 matrices called ‘masks’. matching occurrences of i in X and j in Y , at corresponding B. Watermark Embedding (Encoding) positions. As indicated by Zhang and Srihari [44], there exist several measures that can be used to evaluate the similar- Once generated the masks from nonuplets, we use the set of ity, S(X; Y ), between X and Y . Among these similarity triplets to encode the color information into the masks. First, measures, the most common are Dice, Jaccard-Needham, we compute the halftone of each color channel independently, Sokal-Sneath, Kulzinsky (Matching), Rogers-Tanimoto, Sokal- generating R, G, and B. For each pixel in these planes, we Michener, Russell-Rao, and Yule.